Division algebras and MRD codes from skew polynomials

Thompson, D.; Pumplün, S.

Abstract

Let be a division algebra, finite-dimensional over its center, and a skew polynomial ring. Using skew polynomials, we construct division algebras and maximum rank distance codes consisting of matrices with entries in a noncommutative division algebra or field. These include Jha Johnson semifields, and the classes of classical and twisted Gabidulin codes constructed by Sheekey.

Citation

Thompson, D., & Pumplün, S. (2023). Division algebras and MRD codes from skew polynomials. Glasgow Mathematical Journal, 65(2), 480-500. https://doi.org/10.1017/S001708952300006X

• Journal Article Type: Article
• Acceptance Date: Feb 28, 2023
• Online Publication Date: Apr 20, 2023
• Publication Date: 2023-05
• Deposit Date: Feb 28, 2023
• Publicly Available Date: Oct 21, 2023
• Journal: Glasgow Mathematical Journal
• Print ISSN: 0017-0895
• Electronic ISSN: 1469-509X
• Publisher: Cambridge University Press
• Peer Reviewed: Peer Reviewed
• Volume: 65
• Issue: 2
• Pages: 480-500
• DOI: https://doi.org/10.1017/S001708952300006X
• Keywords: Skew polynomial ring; skew polynomials; division algebras; MRD codes
• Public URL: https://nottingham-repository.worktribe.com/output/17938098
• Publisher URL: https://www.cambridge.org/core/journals/glasgow-mathematical-journal/article/division-algebras-and-mrd-codes-from-skew-polynomials/DDB038779765ED0C4C06178B0FF7EF4C
• Additional Information: Copyright: © The Author(s), 2023. Published by Cambridge University Press in association with Glasgow Mathematical Journal Trust; License: This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.; Free to read: This content has been made available to all.